You define miracles as that which defy scientific explanation. However, miracles are what are done outside the order of nature. Just because scientific explanations don't exist for some phenomena, doesn't mean those phenomena are miracles (unless you use the word "miracle" figuratively, like when one says "the miracle of life" in reference to natural mysteries like the intricacy of an oak growing from an acorn).

There are natural mysteries, but miracles are supernatural mysteries. (Mysteries are truths we can't exhaustively understand; we can always learn more about them.)

Types of miracles

St. Thomas Aquinas distinguishes the three types of miracles, miracles being "works that are sometimes done by God outside the usual order assigned to things", in Summa Contra Gentiles, lib. 3 cap. 101 (from highest to lowest):

1. "those events in which something is done by God which nature never could do."
2. "those events in which God does something which nature can do, but not in this order"
3. "when God does what is usually done by the working of nature, but without the operation of the principles of nature."

Faith excludes all doubt.

A few relevant canons from Pope Pius IX, First Vatican Council, dogmatic constitution Dei Filius on faith & reason, canons on faith:

The certainty of miracles:

Canon 4. If any one shall say that miracles are impossible, and therefore that all the accounts regarding them, even those contained in Holy Scripture, are to be dismissed as fabulous or mythical; or that miracles can never be known with certainty, and that the divine origin of Christianity can not be proved by them: let him be anathema.

That supernatural faith does not need scientific demonstration:

Canon 6. If any one shall say that the condition of the faithful, and of those who have not yet attained to the only true faith, is on a par, so that Catholics may have just cause for doubting, with suspended assent, the faith which they have already received under the magisterium of the Church, until they shall have obtained a scientific demonstration of the credibility and truth of their faith: let him be anathema.

As the Catechism of the Council of Trent (pt. 1 The Creed, article 1 "I Believe") says, faith excludes all doubt and curiosity:

Faith Excludes Doubt
The knowledge derived through faith must not be considered less certain because its objects are not seen; for the divine light by which we know them, although it does not render them evident, yet suffers us not to doubt them. For God, who commanded the light to shine out of darkness, hath himself shone in our hearts (2 Cor. 4:6), that the gospel be not hidden to us, as to those that perish. (2 Cor. 4:3).

Faith Excludes Curiosity
From what has been said it follows that he who is gifted with this heavenly knowledge of faith is free from an inquisitive curiosity. For when God commands us to believe He does not propose to us to search into His divine judgments, or inquire into their reason and cause, but demands an unchangeable faith, by which the mind rests content in the knowledge of eternal truth. And indeed, since we have the testimony of the Apostle that God is true; and every man a liar (Rom. 3:4), and since it would argue arrogance and presumption to disbelieve the word of a grave and sensible man affirming anything as true, and to demand that he prove his statements by arguments or witnesses, how rash and foolish are those, who, hearing the words of God Himself, demand reasons for His heavenly and saving doctrines? Faith, therefore, must exclude not only all doubt, but all desire for demonstration.

Even Aristotle argued that not all truths are demonstrable*, and St. Thomas Aquinas even showed in Summa Theologica II-II q. 2 a. 4 that "it is necessary to believe those things which can be proved by natural reason".
^{*cf. quote in this Philosophy StackExchange question}

It's a futile endeavor to try to give naturalistic explanations to everything (the heresy of naturalism), since there are supernatural realities, and "giving assent to the truths of faith is not foolishness, even though they are above reason".

Does the Catholic Church attempt to explain scientifically any miracles associated with Jesus' time on earth?

I strongly suspect that the answer is no (I am not a Catholic).

Supernatural miracles are by definition, outside the scope of science, generally.

Supernatural or Science: How Do We Explain Miracles?

AIG here explains that there are 'miracles of timing' i.e. events and processes that say, occur despite their exceeding improbability.

There are also 'supernatural miracles'. There may be other forms, but generally they would fall into one of these broad categories.

Miracles of timing would be explained by science in the way that any other natural phenomenon would be explained, except to say that they are a miracle by nature of their improbability and perfection of their timing.

Supernatural miracles would be beyond the scope of science given that they occur in contrast to natural physical law which is what is subject to scientific investigation.

The role of science in investigating miracles would be to say that an event, if it occurs in direct opposition to known physical laws, could be described as a miracle.

To be clear. This is not the same as saying:

'science has no explanation for this event',

but rather

'this is in direct, demonstrable opposition to natural law'

For example,

someone who has been dead for 3 days being brought back to life

or,

an amputated limb being fully and instantly restored (including the neural circuitry and brain chemistry required for it to function correctly).

These are simply supernatural events and definitively beyond the scope of science.

As for the molecular and physical considerations involved in these events, who can say?

The other limitation of science to test miracles is that science requires repeatability and control of variables. Unless you can miraculously, instantly grow back limbs in a controlled, double blind experiment, preferrably in a large sample, then science would be limited in what it could discover about this process.

As Isaiah 55:8-9 states:

(8) For my thoughts are not your thoughts, neither are your ways my ways, declares the Lord. (9) For as the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts.

Does the Catholic Church attempt to explain scientifically any miracles associated with Jesus' time on earth?

I know of no Catholic theologian or Catholic scientist who has attempted to do so with the Biblical miracles performed by Christ.

But it is certainly permitted within the philosophical understandings of the Catholic Church. Just because I do not know of anyone within the Church to have done so: yet.

To be honest here, I would be surprised that no Catholic theologian or scientist has taken up this avenue of research. Just can not find one...

It could stated here that the miracles needed for a beatification or canonization are done by the power of God and by extension Christ who is the Second Person of the Most Holy Trinity.

Revelation 5:8 speaks of 24 elders with golden bowls full of incense, which are the prayers of the saints, but Catholics are not as wedded to the text of Scripture as in other denominations. It is a long tradition, that some Protestants would argue is not unbiblical, that deceased Christians pray for and can even, through the power of God, work miracles for, the living.

Pope St. John Paul II’s encyclical letter Fides et Ratio gives the faithful a way to understand scientific research in the domain of faith, when trying to understand the Mysteries of Faith such as the Resurrection of Christ. Scientific research into the miracles of Jesus must follow clear guidelines in order to remain valid forms of research and investigation.

It may help, then, to turn briefly to the different modes of truth. Most of them depend upon immediate evidence or are confirmed by experimentation. This is the mode of truth proper to everyday life and to scientific research. At another level we find philosophical truth, attained by means of the speculative powers of the human intellect. Finally, there are religious truths which are to some degree grounded in philosophy, and which we find in the answers which the different religious traditions offer to the ultimate questions. (30)

The more influential of these radical positions are well known and high in profile, especially in the history of the West. It is not too much to claim that the development of a good part of modern philosophy has seen it move further and further away from Christian Revelation, to the point of setting itself quite explicitly in opposition. This process reached its apogee in the last century. Some representatives of idealism sought in various ways to transform faith and its contents, even the mystery of the Death and Resurrection of Jesus, into dialectical structures which could be grasped by reason. Opposed to this kind of thinking were various forms of atheistic humanism, expressed in philosophical terms, which regarded faith as alienating and damaging to the development of a full rationality. They did not hesitate to present themselves as new religions serving as a basis for projects which, on the political and social plane, gave rise to totalitarian systems which have been disastrous for humanity. (46)

In the field of scientific research, a positivistic mentality took hold which not only abandoned the Christian vision of the world, but more especially rejected every appeal to a metaphysical or moral vision. It follows that certain scientists, lacking any ethical point of reference, are in danger of putting at the centre of their concerns something other than the human person and the entirety of the person's life. Further still, some of these, sensing the opportunities of technological progress, seem to succumb not only to a market-based logic, but also to the temptation of a quasi-divine power over nature and even over the human being. (46)

Finally, I cannot fail to address a word to scientists, whose research offers an ever greater knowledge of the universe as a whole and of the incredibly rich array of its component parts, animate and inanimate, with their complex atomic and molecular structures. So far has science come, especially in this century, that its achievements never cease to amaze us. In expressing my admiration and in offering encouragement to these brave pioneers of scientific research, to whom humanity owes so much of its current development, I would urge them to continue their efforts without ever abandoning the sapiential horizon within which scientific and technological achievements are wedded to the philosophical and ethical values which are the distinctive and indelible mark of the human person. Scientists are well aware that “the search for truth, even when it concerns a finite reality of the world or of man, is never-ending, but always points beyond to something higher than the immediate object of study, to the questions which give access to Mystery”. (106)

The miracles performed by Christ, like the miracles needed in the cases of beatification and canonization are events that go beyond the forces of nature, which are realized by God outside of what is normal in the whole of created nature.

"For the beatification of a servant of God who is not a martyr, the Church requires a miracle; for canonization, including that of a martyr, it requires another," he explained. "Only the presumed miracles attributed to the intercession of a servant of God or of a blessed 'post mortem' can be the object of verification."

A miracle is an "event that goes beyond the forces of nature, which is realized by God outside of what is normal in the whole of created nature by the intercession of a servant of God or a blessed," Monsignor Di Ruberto said.

The investigation of a miracle is carried out separately from that of virtues or martyrdom.

Consequently, the recognition of a miracle "makes it possible to grant with certainty permission for devotion," he added. Hence, the "capital importance of keeping miracles as a requirement in the causes of canonization."

A collegial body made up of five medical specialists and two professional experts form the Medical Consultation, in charge of the scientific examination of the presumed miracle. Their judgment is of a "strictly scientific" character, so their being "atheists or of other religions is not relevant," Monsignor Di Ruberto emphasized.

"Their examination and final discussion are concluded by precisely establishing the diagnosis of the illness, the prognosis, the treatment and its solution," he continued. "To be considered the object of a possible miracle, the cure must be judged by the specialists to have been rapid, complete, lasting and inexplicable, according to present medical-scientific knowledge."

The miracle might go beyond the capacities of nature in regard to the substance or the subject of the event, or the way it occurred.

So a distinction is made of three great miracles: the resurrection of the dead; the complete cure — which might entail the reconstruction of organs — of a person judged incurable; or the curing of an illness — which could be cured over time but takes place instantly.

"If there are uncertainties, the consultation suspends the evaluation and asks for more experts or documentation," Monsignor Di Ruberto said. "Once there is a majority or unanimity in the voting, the examination is sent to the theologians' consultation."

Starting with the conclusions of the Medical Consultation, the theologians "are called to identify the nexus of causality between prayer to the Servant of God and an inexplicable cure or technical success, and they express the judgment that the prodigious event is a real miracle."

"When the theologians have also expressed their vote in writing, the assessment is sent to the Congregation for Bishops and cardinals who, after hearing the exposé of a 'speaker,' discuss all the elements of the miracle," the monsignor said. "Each component, therefore, gives his judgment, which must be submitted for the approval of the Pope."

Finally, it is the Holy Father who "determines the miracle and decides on the promulgation of the decree," the monsignor said. The latter is a juridical act of the Congregation for Sainthood Causes, sanctioned by the Pope, "by which a prodigious event is defined as a genuine miracle," he concluded. - Why Miracles Are Required for Canonizations

Scientific research into the Biblical miracles performed by Jesus should have as as an object to gain deeper and more clear understanding of Christ’s life and works while amongst men. It is not a question of trying to draw doubt one these issues. This remains a viable and valid form of genuine Catholic scientific research by Catholics researchers of the truths within our holy religion. Truth has nothing to fear.

The following articles may be of interest to some:

• Miracles of Christ: They may be divided into five classes: nature miracles; miracles of healing; deliverance of demoniacs; victories over hostile wills; cases of resurrection.
• Does It Make Sense To Believe Saints Can Work Miracles?